Maximizing the number of mixed packages subject to variety constraints

We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The specific application is the allocation of excess of a population of various ty...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computers & operations research Jg. 26; H. 13; S. 1323 - 1333
Hauptverfasser: Robb, David J., Trietsch, Dan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Elsevier Ltd 01.11.1999
Elsevier Science
Pergamon Press Inc
Schlagworte:
Algorithms
Applied sciences
Bin packing
Christmas
Exact sciences and technology
Greeting cards
Mathematical programming
Operational research and scientific management
Operational research. Management science
Operations research
Packaging
Polynomial algorithm
Pseudo-polynomial
Seasonal products
Studies
Style goods
Seasonal products
Bin packing
Style goods
Polynomial algorithm
Pseudo-polynomial
Integer programming
Maximization
Constraint
Optimal solution
Bin packing problem
Variety
Polynomial time
ISSN:0305-0548, 1873-765X, 0305-0548
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The specific application is the allocation of excess of a population of various types of cards (e.g., left over from a previous selling season) to fixed-sized “variety packs” which guarantee a given level of variety (i.e., no more than k of any type of card). Some card types with large numbers (perhaps the most unpopular from the previous season) may have to be discarded to preserve the variety constraint. The method developed employs a test for feasibility of a given number of packs and includes a simple allocation procedure. A numerical example is provided along with (worst-case) complexity calculations. In addition, we solve a practical problem in which an organisation marketing Christmas cards sought to determine the impact of pack size and variety level on the level of unallocated cards. Scope and purpose Organisations involved in the stocking and sale of seasonal “style” items such as greeting cards, may periodically face excess stock of various items (e.g., from previous seasons), and may decide to market the items in packs guaranteed to contain a certain degree of variety. Our objective in this paper is to show how to maximise the number of card packs that can be formed from an assortment of excess stock, where there is a marketing-based variety constraint restricting the number of each type of card in each pack. The solution procedure developed is intuitively appealing and can be easily implemented on a spreadsheet. In addition to presenting a numerical example, we provide results from the application and implementation of the method in the card sales operations of a charitable organisation. The method could also have broader application in other settings where variety is sought – such as in groups or teams.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/S0305-0548(98)00105-1